(Mostly) Classical physics - PowerPoint Presentation

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(Mostly) Classical physics of neutron star magnetic fields

Andreas ReiseneggerInstituto de AstrofísicaPontificia Universidad Católica de Chile

Workshop

«

Astro-solids, dense matter, and gravitational waves»Institute of Nuclear Theory, U. of Washington, Seattle16-20 April 2018

Slide2

«ANSWERS»

group (as of 2016)Astrophysics

of Neutron Stars With Extra/Exotic/

Energetic/Extreme Related Stuffhttp://www2.astro.puc.cl/answers/

Funding:FONDECYT Regular

Grant

1150411

Rotational

& magnetic effects in neutron stars and beyond (2015-2019)FONDECYT postdoctoral grants, CONICYT PhD FellowshipsPFB-06 Center for Astronomy & Associated Technologies (CATA)

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Outline

Composition

gradients

& stable stratification Hydromagnetic equilibria & stabilityProcesses in the neutron star crust: Hall + OhmCore B evolution: eroding stable stratificationApplication: weak B of LMXBs & MSPs

Conclusions

&

discussion

Slide4

Magnetic field in neutron stars??

In vacuum (lab), neutrons decay with half-life ~ 15 min:In dense, degenerate matter, low-energy quantum states are filled (blocked) “Chemical” (weak interaction) equilibrium:

Around nuclear density, neutrons coexist with some protons & electrons: Density-dependent fraction, few %Charged & degenerate: currents flow with very little resistance

 Magnetic field “frozen in” for a long time (Baym et al. 1969)

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Composition gradient in NS

core

Possible

e

quilibrium particle populations in very dense matter Glendenning,Compact Stars, p. 239

Slide6

Stratification & buoyancy

Non-barotropic fluid:

blob displaced from equilibrium “remembers” where it came from,

through its composition (in NSs) or specific entropy (main sequence, WDs)

Brunt-Väisälä

(buoyancy)

frequency> 0: stable oscillations (“g-modes”)< 0: unstable



convection

= 0: neutrally stable (“barotropic”)

“Ledoux criterion”

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Stable stratification vs. B

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Hydromagnetic equilibria 

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Axially symmetric equilibriaPoloidal+toroidal decomposition:

2 scalars  (r, ) & 

(r, ) Each component independently satisfies

No fluid forces in  - direction: Thus,

2 types of toroidal “magnetic surfaces” of constant  &  :closing outside the star:  = 0: pure poloidal field

closed

inside

the star:   0: twisted toroidal field

Braithwaite 2007

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Stability??

Purely toroidal (azimuthal) fields are unstable

Flux rings “repel” each other (Tayler 1973)

Figure

from Spruit 1999

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Purely poloidal (meridional) fields

are also unstable

Braithwaite 2008

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Stable MHD equilibria

MHD

simulations

:

(Braithwaite & Spruit 2004, 2006; Braithwaite 2009)Self-gravitating balls of conducting fluidStably stratified by an entropy gradientDisordered initial BGeneric outcome ~ axially symmetric: Poloidal & toroidal B

components

stabilize

each other

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Effect of stable stratification

Mitchell, Braithwaite, Reisenegger, Spruit, Valdivia, & Langer 2015 Random initial B Ordered initial B

(twisted torus)

Warning:

Ratio of diffusive/Alfvén time strongly reduced in the simulations!

In

stably stratified

stellar models, we find configurations that decay slowly (~diffusion time

 MHD-stable) & others that decay quickly (~Alfvén time  unstable). In barotropic models, all configurations explored decay quickly.

Diffusion

only

Stable

Strat.

Barotropic

Stable

Strat.

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Stability condition &

hidden energy

(

Very

rough) conditions for mutual stabilization of Bpol vs. Btor :

Braithwaite

2009; Marchant+ 2011; Akgün+ 2013; Mitchell+ 2015



Possibly strong, hidden toroidal BEnergy reservoir for magnetars (Thompson & Duncan 2001), especially «low‐B magnetars» (Rea+ ‘10, ‘12, ‘13)Non‐uniform surface temperature on CCOs (Shabaltas & Lai 2012)Continuous gravitational waves (Cutler 2002; Mastrano+ 2011; many more)

 

Will

these

equilibria

live

forever

?

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Solid NS crust: Hall + Ohm

 

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NS crust: Hall drift

Hall drift non-linear  “turbulent

cascade” to small scales

? (Goldreich & R. 92)Analytic solutions:Current

sheets (Vainshtein et al. 2000; Reisenegger et al. 2007)Large-scale Hall equilibria (Gourgouliatos et al. 2013)Numerical 2D (= axial symmetry): Stable Hall equilibria = “attractors” (Gourgouliatos & Cumming 14a,b; Marchant et al. 14; Cumming et al. in prep.); braking indices n<3 (Gourgouliatos & Cumming 14c)

Coupled

thermo-magnetic

evolution: Viganò et al. 13Numerical 3D: Attractors appear to survive (Wood & Hollerbach 15)All this assumes that the magnetic flux goes only through the crust

Unlikely

unless

a

core

superconductor can

expel

the

flux (time

scale

???)

Either

way

,

need

to

study

processes

in

the

core

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(Multi-)

fluid core

B pushes on the fluid (charged particles): Can it escape??Not trivial: Stable stratification (composition gradient) prevents (or strongly constrains) bulk motions.Ways out:

Bulk motion with “real-time” composition adjustment through beta decays (mUrca): n  p + e Effective at high T (& B): magnetars (Thompson & Duncan 1996)

Ambipolar diffusion (solenoidal mode): Relative motion of 2 fluids: neutrons & charged particles (frozen to B) against their mutual collisions Effective at low T: old NSs ~ progenitors of LMXBs & MSPs? [Time scales: Goldreich & R. 1992; 1D sim.: Hoyos, R., & Valdivia 2008, 2010]

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Simulation (Castillo+ 2017): axial

symmetry (meridional cut) charged particles & B moving

against a fixed, uniform neutron backgroundMagnetic

field Density/pressure Velocity field

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Simulation results & discussionB evolves towards twisted-torus equilibria

 No full decayBUT: Still to be included

:Radial density gradientsNeutron motionAdditional particle

speciesSuperconductivity (type I or II??) & superfluidity3D effects: likely instabilities!

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Low B in MSPs & LMXBs

Standard explanation:

«Recycling» via

accretion reduces not only

P, but also B, through either:1) Accretion

heating



enhanced crustal resistivity (Shibazaki+ 1989): requires B not to penetrate the core2) Diamagnetic

screening

by

accreted

material (

Bisnovatyi-Kogan

&

Komberg

’74; Melatos++;

many

others

):

instabilities

??

(

Mukherjee

+ 2013)

Alternative

(

toy

model

-- Cruces, R., & Tauris, in

prep

.):

Spontaneous

decay

by

ambipolar

diffusion

of

core

field

in

cold

pre-

accretion

phase

(

requires

crust

to

«

cooperate

»)

Time

available

~

companion’s

main

sequence

lifetime



infer

from

remnant

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Magneto-roto-thermal evolution

Massive

, short-

lived companion(now neutron

star)Low-mass, long-lived companion(now He white dwarf)Cruces, R., & Tauris, in preparation

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Magnetic fields of binary pulsars

Histogram: Binary pulsars

not in globular clusters

Shaded bands:

Rough estimates of expected fields for ambipolar diffusion for each companion

type

,

with

(companion’s main sequence lifetime) – (NS cooling time) (106 yr) = (ambipolar diffusion time)

Caveats

:

Several

outliers

:

unusual

binary

evolution

?

P

redictions

similar

to

«

standard

»

accretion-induced

decay

model

Slide23

Conclusions & discussion

B

fields

are «weak» (ε ~ 10-6 B152)Their stability depends on:Linked poloidal & toroidal componentsStable stratification of core matter  Allows for a strong, hidden toroidal component

Secular

evolution

through non‐ideal MHD processes:Ohmic resistivity in the crustNon-linear Hall dynamics in the crustErosion of stable stratification in core  destabilization of equilibria  Explanation of weak MSP/LMXB fields?Still no full simulations or understanding:3D instabilities?Ubiquity & effects of superfluidity or superconductivity?